Xiao-Min Cao
Abstract:
This article concerns a nonlinear system modeling the bending vibrations
of a nonlinear beam of length
. First, we derive the existence of
long time solutions near an equilibrium. Then we prove that the nonlinear
beam is locally exact controllable around the equilibrium in
and with control functions in
. The approach we used are open
mapping theorem, local controllability established by linearization,
and the induction.
Submitted May 4, 2015. Published September 17, 2015.
Math Subject Classifications: 93B05, 35L75, 93C10, 93C20.
Key Words: Nonlinear beam equation; locally exact controllability;
equilibrium; smooth control.
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Xiao-Min Cao School of Mathematical Sciences Shanxi University Taiyuan 030006, China email: caoxm@sxu.edu.cn |
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